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INTERNATIONAL JOURNAL OF
MARITIME TECHNOLOGY IJMT Vol.9/ Winter 2018 (23-32)
23
Available online at: http://ijmt.ir/browse.php?a_code=A-10-901-1&sid=1&slc_lang=en
Investigation of the Effect of Local Buckling and VIV Fatigue on Failure
Probability of Subsea Pipelines in Iranian South Pars Gas Field
Abdolrahim Taheri1*, Mohammad Mahdi Shabani2, Mohammad Daghigh3
1 Assistant Professor of Offshore Structural Engineering Department, Petroleum University of Technology (PUT);
[email protected] 2 MS.C. Student in Offshore Structural Engineering, Petroleum University of Technology (PUT);
[email protected] 3 Assistant Professor in Offshore Engineering, Pars Oil and Gas Company (POGC); [email protected]
ARTICLE INFO ABSTRACT
Article History:
Received: 5 Aug. 2017
Accepted: 8 Jan. 2018
Free-span occurs normally in a pipeline at uneven seabed, dynamic seabed and
pipeline crossing. Free spanning in pipeline causes Vortex Induced Vibration
(VIV) fatigue, fracture and bursting. In this paper, a pipeline located in South
Pars Gas Field is assessed against local buckling and VIV fatigue using
probability of failure theory based on the recommended methodology by Det
Norske Veritas (DNV) corresponding to different soil classes and different
span length to pipeline diameter and also different water depths by applying
First-Order Reliability Method (FORM) and Monte-Carlo Sampling (MCS),
separately. Furthermore, the simultaneous effect of local buckling and VIV
fatigue is assessed in terms of probability of failure. Finally, in order to
determine the effect of each parameter on failure probability, sensitivity
analysis is carried out using the alpha index.
Keywords:
subsea pipeline
probability of failure
free span
local buckling
Figure 1. Different types of pipeline hazards[2]
1. Introduction Marine pipelines, a complex system comprises a total
length of thousands of kilometers, have been the most
practical and low price means of transporting
hydrocarbon including oil, gas, condensate and their
mixtures in the offshore oil and gas industry[1]. The
subsea pipelines are exposed to hazards like extreme
weather conditions, collision with vessels, trawl impact
and pipeline span (see Figure1)[2].
Subsea pipelines are subjected to various types of
phenomena, like fatigue, corrosion, etc. which cause
pipeline failure and should be monitored to guarantee
the safety of pipeline [2]. According to DNV-OS-F101,
fatigue assessment of pipeline must be performed at
any stages (i.e. installation and operation)[3]. The free
spanning as one of the important causes of fatigue
occurs due to seabed unevenness, changes in seabed
topology, artificial supports and scours [1], [4].
Furthermore, as water depths increases, deteriorative
effect of local buckling on the pipeline health and
integrity of offshore pipeline highlights. However,
DNV recommends
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some methodologies for assessing health of a
submarine pipeline against local buckling and VIV
fatigue separately, but in previous studies like
Hagen[5], Abeele[6] and Shabani[7], simultaneous
effect of VIV fatigue and local buckling was not
considered.
In this paper, Probability of Failure (POF) of a pipeline
based on DNV’s recommended methodology,
considering local buckling (considering combined load
scenario) and free spanning using FORM and MCS is
determined separately for a pipeline located in Iranian
South Pars Gas Field. Furthermore, accuracy of FORM
is tested in different conditions. As in previous studies,
simultaneous effect of local buckling and VIV fatigue
was not considered, therefore POF of the pipeline
considering both conditions are determined. Finally, in
order to assess the effect of each parameter on POF,
sensitivity analysis is carried out using alpha index.
2. Pipeline analysis 2.1. Free span The vortex shedding frequency caused by a flow
normal to a free span is governed by the pipeline outer
diameter, the current velocity, and the Strouhal’s
number. Once the shedding frequency reaches the
natural frequency of a span, it starts to vibrate and VIV
occurs[4]. The free span may induce the pipeline
vibration due to vortex shedding which may eventually
cause pipeline fatigue damage. Therefore, free span
analysis is quite a fundamental aspect of the subsea
pipeline design and operation. Because free span length
limitation and fatigue damage are usually
associated with substantial cost for the free span
intervention due to the deep water depth and great
seabed instability/unevenness[8]. In order to determine fatigue life capacity of a pipeline
based on DNV code, following procedure should be
followed (see Figure 2). In Figure 2, L is the span
length, D is pipeline outside diameter (considering
coating layer), Uc is current velocity amplitude and Uw
is the significant wave-induced velocity amplitude.
DNV divided free spanning pipeline behavior into
three categories based on ratio of span length to
pipeline diameter; beam dominant behavior (for
03<L/D<100), combined beam and cable behavior (for
100<L/D<033) and cable dominant behavior (for
L/D>033)[8]. In the first category, pipeline response
can be estimated by deterministic theories, i.e.
Bernoulli’s beam theory. However, in second and third
classes beam theory is not applicable and dynamic
response must be predicted by solving equation of
motion (more detailed information is given in reference
[9]).
In order to perform VIV fatigue assessment, it is
necessary to choose an appropriate fatigue criterion.
The most popular fatigue criteria are displayed in
Figure 3.
Figure 2. VIV fatigue assessment procedure[1,4,5]
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Traditional Stress-Based Approach
strain-based approachfracture mechanics approach
Major approaches
for fatigue analysis
Figure 3. Major approaches for analyzing and designing
fatigue[11]
DNV recommends application of stress-based
approach [8], [12]. Main method for determining
fatigue damage in stress-based approach is S-N curve
[13]. Because of dependency of results on soil stiffness,
soil characteristics should be determined using
recorded data from site. In case of insufficient detailed
information about seabed characteristics, DNV
recommended to consider following models for
calculating soil stiffness [8]:
2 1
1 3 3
v sV
CK D
(1)
2 1
13 3
sL LK C D
(2)
where VK and LK are vertical and horizontal stiffness,
vC and LC are dynamic stiffness factors in vertical
and horizontal directions, respectively. is Poisson’s
ratio, s is soil density and is water density. The
value of the above parameters can be determined from
DNV-RP-F105[8], [14].
2.2. Local buckling Main load effect on subsea pipelines is bending
combined with longitudinal force while subjected to
external hydrostatic pressure during installation and
internal pressure in operational phase[16]. A pipe
subjected to bending may fail due to local buckling,
collapse, or fracture, but it is local buckling or collapse
limit state that commonly dictates the design. Local
buckling and collapse strength of metallic pipes have
been the main subjects for many studies in subsea and
civil engineering, such as Murphey and Langner[17],
Gresnigt[18], Mohareb et al.[19], and Bai et al.[20],
[21].
The limit bending moment for steel pipes depends on
many parameters. The major factors are given here in
arbitrary sequence:
1. Diameter over wall thickness ratio.
2. Material stress-strain relationship.
3. Material imperfections.
4. Welding
5. Initial out-of-roundness.
6. Reduction in wall thickness
7. Cracks (in pipe or welding).
8. Local stress concentrations due to, say,
coating.
9. Additional loads and their amplitude.
10. Temperature
Several formulations have been proposed for
estimating collapse pressure like Timoshenko and
Gere’s[22], Haagsma and Schaap’s[23] and etc. [3],
[16], [24]. Both Timoshenko and Haagsma models
account for initial out of roundness[16]. DNV-OS-
F101 uses Timoshenko and Gere’s equation. DNV
proposed two different conditions for pipeline collapse;
overcoming external pressure as dominant factor and
considering the combined effect of internal pressure,
external pressure and axial force[3]. In order to
determine collapse pressure due to combined loading
effect, DNV proposed the following model;
2
2
2
2
2
2
| M |. .
.
. .
.
. 1.
Sdm SC
c P
m SC Sd i
c P
i eP
c b
M t
S p
S t
p p
P t
(3)
Where MSd is the design moment (which can be
determined by Eq.(4)), SdS is design axial force (which
can be determined by Eq.(5)), ip is internal pressure,
bP is bursting pressure (which can be found out by
Eq.(6)), PS and PM are plastic capacity of pipeline
against axial force and bending moment (which can be
determined by Equations (7) and (8) , respectively),
ep is external pressure, m and SC are material
resistance factor and safety class resistance factor,
respectively, c and P are flow stress parameter and
parameter for accounting the effect of D/t2 ratio (which
can be determined by Equations (9) and (10) ,
respectively).
. .
. .
. .
. .
sd F F c
E E E
I F c
A A c
M M
M
M
M
(4)
. .
. . .
. . . .
sd F F c
E E I F c
A A c A A c
S S
S S
S S
(5)
2. 2
. .3
b cb
tp t f
D t
(6)
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. . .p yS t f D t t (7)
2
. .p yM t f D t t (8)
1 . uc
y
f
f (9)
21
3
21 3 1
3
i e
b
p
i e i e
b b
p p
p
p p p p
p p
(10)
And in the Eq. (10), β is a parameter for considering
effect of D/t2 which can be determined by Eq. (11)
[3].
2
60
90
Dt
(11)
Also in Eq. (4) and Eq. (5) c , F , E and A are
condition load effect factor, functional load effect,
environmental load effect and accidental load effect,
respectively. As the contractor company (i.e. TOTAL
Company) considered combined loading condition for
assessment of pipeline against local buckling, current
paper deals with combined loading condition.
3. Reliability assessment 3.1. Reliability method
Reliability of a component can be defined as the
probability that it meets some specified requirements
under special environmental conditions [25].
Reliability methods as a mathematical tool, are used for
determination of POF in some special conditions by
considering uncertainties in both load and resistance
parameters [6]. Uncertainties can be divided into two
main categories including epistemic and aleatoric[26].
Epistemic type is related to the measurement errors,
limited sample numbers, or calibration of equipment,
while aleatoric type is related to the nature of material
or nature of phenomena. Aleatoric uncertainties, unlike
the epistemic uncertainties, cannot be excluded by
increasing the number of samples or calibrating the
measurement’s tools [27]. System reliability is defined as the probability that the
system will not attain the specified limit state.
Generally, performance function or Limit State
Function (LSF) g(X) is defined by the stochastic loads
L(X) and resistance R(X) as the condition where load
equals (or bigger than) the system’s resistance:
g X R X L X (12)
Mathematically, it is more suitable to calculate the
reliability of a system in terms of its complements [6],
[28]
0
0f R L
g
P P g f x f x dx
(13)
Where Rf and
Lf are probability density functions for
resistance and load, respectively. Reliability index
(RI) is defined as:
1
fP (14)
where Φ is standard normal (cumulative) distribution
function. POF and RI can be determined by FORM and
MCS[29], [30].
3.2. Case study
In present study, reliability assessment is carried out for
a pipeline located on South Pars Gas Field with the
specifications presented as follows:
Table 1. Pipeline specification
Parameter value Unit
Pipe class API-5L-X65
Pipeline Wall
Thickness(PWT)
24 Mm
Pipeline outside diameter 816.8 Mm
Fluid type Natural Gas
Fluid density 110 3
Kgm
Steel density 7850 3
Kgm
Water depth(maximum) 85 M
Elasticity Modulus 210 GPa
SMYS 448 MPa
SMTS 540 MPa
Operating Pressure(OP) 13.5 MPa
Ovality 0.5%
Submerged weight in
operating condition
4273 Nm
Production Wet gas
Environmental condition of pipeline installation site is
approximately stable and its variation is small. Current
speed varies from 0.5m/sec to 0.6m/sec in the worst
condition (with one year and 100 years return period,
respectively) and also effect of wave-induced flow on
the oscillation amplitude is small and it can be
neglected.
Pipeline seabed’s profile is presented as follows:
Figure 4. Seabed profile
A
B
C
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It can be found from Figure 4 that variation in slope of
seabed is too much and in some points, (e.g. A) there
are spans where free spanning may occur. However,
designer company has not considered effect of VIV
fatigue for the pipeline which is probable using above
seabed profile for the pipeline. The present study
assesses probability of occurrence of VIV fatigue for
the pipeline.
3.3. Target safety
When the structural reliability analysis is needed to be
carried out, a target safety level should be selected in
order to ensure that a certain safety level is always
achieved. For different probable scenarios, DNV-OS-
F101 recommends suitable target safety levels which
are presented in Table 2. As free spanning belongs to
the FLS and ULS categories and the designer was
considered safety level as high class. Therefore, the
target POF for satisfying the target safety level is
adopted as POF=10-5.
Table 2. target POFs vs. target safety levels[3]
Lim
it state
categ
ories
Limit state
Safety class
Lo
w
Med
iu
m
Hig
h
Very
hig
h
SLS all 10-2 10-3 10-3 10-4
ULS Pressure
containment
10-4
to
10-5
10-5
to
10-6
10-6
to
10-7
10-7
to
10-8 ALS
ULS All other
10-3
10-4
10-5
10-6 FLS
ALS
3.4. Limit State Function
3.4.1. Free spanning
A comprehensive reliability analysis for free spanning
subsea pipelines is presented in reference [5]. In this
paper, in-line VIV fatigue is performed. Limit State
Function (LSF) is used for fatigue failure after T years
which can be expressed as follows;
( ) 25
86400*365fatT T
g T
(15)
Where fatT is the pipeline fatigue life capacity which
can be determined by Eq.(16) and is usage factor
which can be determined using DNV-RP-C203 and cum
fatD is cumulative fatigue damage that can be
calculated by Eq. (17) [8], [12]. However DNV
recommends that pipeline design life should be
considered at least for 25 years [2], [3].
cumfatfat
T TD
(16)
1
kcum ifat
i i
nD
N
(17)
In addition to the above LSF, the Palmer-Miner index
can be used to develop another LSF for reliability
assessment of free spanning pipelines (see Eq. (18))
[6].
1 cum
fatg x D (18)
3.4.2. Local buckling
In order to choose an appropriate LSF for local
buckling, using DNV’s recommended equation for
assessment of pipeline collapse under combined
loading (Eq. (3)) and TOTAL’s design documentation,
the following LSF is chosen for reliability assessment
of pipeline collapse under combined loading.
2
2
2
2
2
2
| M |. .
.1
. .
.
..
Sdm SC
c P
m SC Sd i
c P
i eP
c b
M tg
S p
S t
p p
P t
(19)
For positive values of g, pipeline can continue a safe
operation, and in other situations, pipeline failure will
occur.
3.5. Uncertainties
Uncertainties which are considered for reliability
assessment are described in Table 3 with their relevant
mean value and Coefficient of Variation (C.O.V).
Distribution types and their relevant parameters are
mentioned in Table 3 which and are based on
recommendation of following references [6], [25]. Table 3. Uncertainties of parameters with their relevant mean
and C.O.V Row Parameter Distribution
Type
Mean C.O.V
1 PWT Normal 0.024 0.05
2 Concrete
coating layer
Normal 0.05 0.1
3 Pipeline span Weibull Variable Variable
4 Pipeline
diameter
Normal 0.8168 0.05
5 Young’s
modulus
Log-normal 210×109 0.05
6 S-N curve
scaling
parameter
Normal 1 0.3
7 Soil stiffness Normal Variable Variable
8 Water depth Weibull Variable Variable
9 Internal
pressure
Normal 13.5x106 0.1
10 S-N curve
scaling
parameter
Normal 1 0.3
11 Fy Normal 448×106 0.1
12 Fu Normal 540×106 0.1
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4. Result and discussion In order to assess the pipeline integrity against
mentioned failure modes, safety of pipeline against
each failure modes are assessed separately. Afterwards,
simultaneous effect of local buckling and free spanning
is considered and pipeline safety is assessed in terms of
POF. Results of each failure modes and their relevant
consequences are presented and discussed in the
following sections;
4.1. VIV fatigue
Using the recommended LSF (Eq. (15)) and
considering the presented uncertainties in Table 3 and
also using the pipeline specifications mentioned in
Table 1, POF is determined with respect to six clay
classes and three sand types and also different L/D
ratios. Table 5 & Table 6 show the relationship between
POF and L/D for different seabed clay and sand types.
Table 4. POF for different L/D and clay types
Response dominated by combined beam and cable
behavior
L/D 110 120 150
Clay Type
FO
RM
MC
S
FO
RM
MC
S
FO
RM
MC
S
Very Soft
Clay 0 0 0 0 0 0
Soft Clay 0 0 0 0 0 0
Firm Clay 0 0 0.0 0.0 1.93e-9 1.79e-9
Stiff Clay 0 0 2.67e-7 2.48e-7 5.13e-2 3.97e-2
Very Stiff
Clay 0 0 1.88e-2 1.80e-2 9.78e-2 9.76e-2
Hard Clay 0 0 3.43e-2 3.29e-2 9.84e-2 9.83e-2
It is obvious from Table 4 that no failure will occur in
beam dominant response behavior (30<L/D<100) and
for very soft and soft clay classes. For larger L/D,
FORM’s results approach to the MCS’s results;
therefore, FORM analysis can be applicable for larger
ratios of span length to pipeline diameter. Furthermore,
it is noted that POF increases by improving soil
stiffness and POFs of very stiff and hard clays soils are
approximately similar. Also, variation of POF with
respect to different span length to pipeline diameters
and different classes of clay is shown in the following
Figure;
Figure 5. POF for different clay types in combined beam and cable
response behavior domain
Table 5. POF for different L/D and sand types
L/D
Response dominated by combined beam and
cable behavior 110 120 150
Sand
Type
FO
RM
MC
S
FO
RM
MC
S
FO
RM
MC
S
Loose 1.1e-16 0 0.025 0.021 0.053 0.050
Medium 5.1-14 0 0.018 0.016 0.082 0.080
Hard 1.3e-10 0 0.056 0.054 0.095 0.096
It can be found from Table 5 that in comparison with
target safety POF, there is no failure for lower L/D
ratios. Also differences between FORM’s result and
MCS’s result are low in larger ratio of span length to
pipeline diameter. Besides in case of stiffer sands
difference between FORM’s result and MCS’s result
tends to the lowest value. Therefore, FORM can be
applied for the larger span length to pipeline diameter
and its accuracy increases for stiffer sands.
Furthermore, it is noted from Table 5 that for larger
span length to pipeline diameter, POF increases. Also,
variation of POF with respect to different span length
to pipeline diameter ratios and different types of sand
is displayed in the following Figure;
Figure 6. Variation of POF vs. different L/D
Furthermore, changes in importance of each parameter
on POF, regarding different L/D and clay types are
investigated in detail in Figure 7 & Figure 8;
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As shown in Figures 7 and 8, except S-N scaling
parameter, variation of other parameters influences the
alpha index for different L/D. By performing
sensitivity analysis for different L/D, decision makers
will find the right choice to decide which parameter can
provide more resistance for pipeline and by considering
the economic aspects, choose the best option for repair
or even replace.
4.2. Local buckling
Using recommended LSF (i.e. Eq. (19)) and
considering the presented uncertainties in Table 3 and
also using the pipeline specification mentioned in
Table 1, POF is determined corresponding different
water depths. Relationship between POF and different
water depths is shown in the Figure 9;
Figure 8. Variation of POF vs. L/D for sand seabed
Figure 7. Variation of alpha index vs. L/D for sandy soil
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Figure 9. POF of the pipeline vs. different water depth
It can be found from figure 9, that no failure will not
happen for water depth lower than 45 meters. POF for
deeper waters goes up to five percent. Furthermore, it
is noted from Figure 5 that FORM’s results are close to
MCS’s results (considering 10,000,000 samples).
Therefore, FORM can be applied for assessment of the
pipeline against local buckling.
Furthermore, in order to assess effects of each
parameter on POF (using alpha-index) sensitivity
analysis is carried out which its result is presented in
following;
Figure 10. Variation value of importance measurement vs.
water depth
As shown in Figure 10, according to the positive and
negative values of importance measurement, PWT and
pipeline diameter are the most effective capacity and
load parameters, respectively. Furthermore, strength
parameters of pipeline remain constant for different
water depths.
4.3. Combined effect of VIV fatigue and local
buckling
In order to assess health and integrity of pipeline
against combined effect of local buckling and VIV
fatigue, there has been no serious attempt to present a
formulation, there is no successful attempts like[31]
and etc. In some special researches like galgoul[31] it
is shown that VIV fatigue has no serious effect on
buckling behavior of pipeline. Therefore, in this
research free spanning and local buckling are proposed
independent mathematically. According to the set
theory, simultaneous POF of two outcomes can be
determined as follow
*P A B P A P B (20)
Th
erefore, the joint POF of the pipeline against combined
effect of free spanning and local buckling equals to
POF of VIV fatigue times POF of local buckling.
Result of the assessment against combined effect of
VIV fatigue and local buckling is presented in
following;
Table 6. POF of the pipeline for interacted outcomes
considering different clay classes
L/D 120 150
Clay
Type
FO
RM
MC
S
FO
RM
MC
S
Very Soft
Clay 0.0 0.0 0.0 0.0
Soft Clay 0.0 0.0 0.0 0.0 Firm Clay 0.0 0.0 1.01E-10 1.01E-10 Stiff Clay 1.40E-08 1.41E-08 2.69E-03 2.25E-03
Very Stiff
Clay 9.84E-04 1.02E-03 5.12E-03 5.53E-03
Hard Clay 1.80E-03 1.86E-03 5.15E-03 5.57E-03
Table 7. POF of the pipeline for interacted outcomes
considering different sand classes
L/
D 110 120 150
San
d T
yp
e
FO
RM
MC
S
FO
RM
MC
S
FO
RM
MC
S
Lo
ose
0.0 1.42E-05 0.0 1.19E-05 2.77E-05 2.83E-05
Med
ium
0.0 1.02E-04 0.0 9.07E-04 4.29E-03 4.53E-03
Har
d
0.0 3.17E-03 0.0 3.06E-03 4.97E-
03
It can be found from Table 7 that no failure will occur
for the shallow waters (i.e. h<71.5m), and pipeline will
continue a safe operation in those depths. Furthermore,
in comparison with selected target safety POF, pipeline
will remain in safe zone for soft clay soils and lower
span length to pipeline diameter ratio than 120.
Another interesting point is that stiffening soil causes
increase in POF due to combined effect of local
buckling and free spanning. Besides FORM’s result are
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again close to MCS’s results for the stiffer clays and
larger span length to pipeline diameter. Therefore,
FORM can be applied for those conditions.
It can be understood from Table 7 that for values of
span length to pipeline diameter larger than 110 meters,
failure of pipeline would be considered as ineligible,
therefore predicting devices like buckle arrestor should
be used as means of buckling control [3]. Furthermore,
like clay soils, increase in soil stiffness causes increase
in POF. Another interesting point is that FORM can be
applied for all categories of sands because of small
difference between FORM’s results and MCS’s results
(10,000,000 samples).
5. Conclusion In this paper, FORM and MCS were utilized for
determining the reliability of a subsea pipeline located
in South Pars Gas Field, which was exposed to free
span (single span) and local buckling. Six classes of
clay and three sand types, different water depth and
different span length to pipeline diameter were
considered to determine POF of the pipeline.
It is concluded that FORM can be applied for reliability
assessment of spanning pipeline in case of larger span
length to pipeline diameter and stiffer soil seabed.
Furthermore, it can be used for reliability assessment
of the pipeline against local buckling.
It is concluded that, in comparison with selected target
safety POF, for soft soils like very soft clay and soft
clay, no failure will occur. It is also concluded that
pipeline collapse will not affect the integrity of pipeline
and for deeper depths, some prevention measures like
buckle arrestor should be taken.
Furthermore, in this research, free spanning and local
buckling considered as independent phenomena. It is
concluded that, however, in comparison with selected
target safety POF and considering combined effect of
VIV fatigue and local buckling, pipeline failure will
occur; however, its relevant POF is too small which can
be neglected.
Finally, sensitivity analysis using alpha index is carried
out. It is shown that span length and pipeline diameter
are the most effective load and capacity parameters,
respectively.
It is strongly recommended to consider FE models for
investigation accurate interaction between local
buckling and VIV fatigue of pipeline in future works.
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